Analysis of the Widely Linear Complex Kalman Filter

 The augmented complex Kalman filter (ACKF) hasbeen recently proposed for the modeling of noncircular complexvaluedsignals for which widely linear modelling is more suitablethan a strictly linear model. This has been achieved in thecontext of neural network training, however, the extent towhich the ACKF outperforms the conventional complex Kalmanfilter (CCKF) in standard adaptive filtering applications remainsunclear. In this paper, we show analytically that the ACKFalgorithm achieves a lower mean squared error than the CCKFalgorithm for noncircular signals. The analysis is supported byillustrative simulations.